When discounted MAB is useful?
One of the reasons a discount factor is used, is to make sure the reward maximization is a well-defined problem and to make the sum of all rewards convergent.

In the MAB problem, the number of trials is typically finite owing to some sort of budget in the number of trials. Hence, this is less of problem. However, by all means discounts are still valid and helpful in cases where the analysis in asymptotic in the number of trials.